Reducing the sample complexity of solving nonconvex quadratic systems when the signal of interest is sparse or lies in the range of an L-Lipschitz  continuous deep generative model trained by a variational autoencoder (VAE) or generative adversarial network (GAN).

• Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors

Junren Chen*, Shuai Huang*, Michael K. Ng and Zhaoqiang Liu

arXiv:2309.09032, 2023 [PDF]

Rotation-invariant autocorrelation features are extracted from random 2D projections with unknown viewing angles, and then used to reconstruct the 3D protein density model.

• Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown--View Tomography

Shuai Huang, Mona Zehni, Ivan Dokmanić and Zhizhen Zhao

SIAM Journal on Imaging Sciences, 16(3), 1414--1430, 2023 [PDF]

A bespoke Gaussian-mixture distribution is used to model the long-tailed noise distribution in cases of brain hemorrhage and/or calcification in QSM.

• Robust Quantitative Susceptibility Mapping via Approximate Message Passing

Shuai Huang, James J. Lah, Jason W. Allen and Deqiang Qiu

Magnetic Resonance in Medicine, 90(4), 1414--1430, 2023 [PDF] 

The mono-exponential decay model of MR signal is incorporated into a Bayesian approach to recover the R2* map via compressive sensing.

• A Probabilistic Bayesian Approach to Recover R2* map and Phase Images for Quantitative Susceptibility Mapping

 Shuai Huang, James J. Lah, Jason W. Allen and Deqiang Qiu,

 Magnetic Resonance in Medicine, 88, 1624--1642, 2022  [Link]

Under the Bayesian framework, the signal x follows a sparsity-promoting distribution. The distribution parameters are treated as unknown variables and jointly recovered with the signal via Approximate Message Passing.

• Approximate Message Passing With Parameter Estimation for Heavily Quantized Measurements

Shuai Huang, Deqiang Qiu and Trac D. Tran

IEEE Transactions on Signal Processing, 70, 2062--2077, 2022 [PDF] 

A set of points on a line or a loop is reconstructed from their unlabelled pairwise distances via a quadratic formulation.

• Reconstructing Point Sets from Distance Distributions

Shuai Huang and Ivan Dokmanić

IEEE Transactions on Signal Processing, 69, 1811--1827, 2021 [PDF] 

A basin of attraction exists around the global optimum of a nonconvex quadratic system. 

• Solving Complex Quadratic Systems with Full-Rank Random Matrices

Shuai Huang, Sidharth Gupta and Ivan Dokmanić 

IEEE Transactions on Signal Processing, 68, 4782--4796, 2020 [PDF]  

Minimizing the generalized entropy function encourages the concentration of energy towards a few significant entries in the solution.

• Sparse Signal Recovery via Generalized Entropy Functions Minimization

Shuai Huang and Trac D. Tran

IEEE Transactions on Signal Processing, 67(5), 1322--1337, 2019 [PDF]